If you have a person A and a person B, and A replicates by having 2 children, and B replicates by having 16 - then two generations in A's camp has 4 young people in it while B's camp has 256. Should A's family be deprived of earned income to the extent that B replicated with no plan to pay for them?
A's lineage would receive 4/260 of the remuneration, while B's would receive 256/260, near 100% of the remuneration. In support of the premise you may balk at the thought of extra remuneration for harder or better work, but you implicitly endorse the thought of extra remuneration for more familial replication even if producing an extra person on the earth would subtract value from it due to strained resources.
A society without income inequality will not be able to attract workers to essential roles. For example, how will society ensure that doctors are available in unattractive locations? Currently, a higher income can serve as an incentive.
It depends on other conditions. To have equal access to employment and the basic securities of life in a socialist (referring to Marxist definition) framework is great, but capitalism as a socioeconomic system disintegrates with equal income. It is an impossibility under capitalism.
In our current society, money translates into power, income inequality leads to abuse and anxiety.
"The Spirit Level: Why Greater Equality Makes Societies Stronger" by Richard Wilkinson and Kate Pickett,
"The Price of Inequality" by Joseph Stiglitz,
"Capital in the Twenty-First Century" by Thomas Piketty,
You can't just have goal in mind, propose a solution and then disregard any other side consequences. Why would someone go through hell to become a doctor, graduate with $250,000 in loans (on average) and then earn as much money as the person microwaving his food at McDonald's.